Concept of orbital entanglement and correlation in quantum chemistry

TL;DR

This paper refines quantum information concepts in quantum chemistry by distinguishing classical and quantum correlations between orbitals, quantifying entanglement, and analyzing the impact of superselection rules on correlation measures.

Contribution

It introduces a detailed separation of classical and quantum correlations in electronic structure, including the quantification of entanglement and the effects of superselection rules.

Findings

Total orbital correlation is mainly classical.

Superselection rules significantly reduce observed correlations.

Entanglement is less prominent in molecular orbital correlations.

Abstract

A recent development in quantum chemistry has established the quantum mutual information between orbitals as a major descriptor of electronic structure. This has already facilitated remarkable improvements of numerical methods and may lead to a more comprehensive foundation for chemical bonding theory. Building on this promising development, our work provides a refined discussion of quantum information theoretical concepts by introducing the physical correlation and its separation into classical and quantum parts as distinctive quantifiers of electronic structure. In particular, we succeed in quantifying the entanglement. Intriguingly, our results for different molecules reveal that the total correlation between orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding. Our work also shows that implementing the fundamental particle number superselection rule, so far not accounted for in quantum chemistry, removes a major part of correlation and entanglement previously seen. In that respect, realizing quantum information processing tasks with molecular systems might be more challenging than anticipated.